Definition:Concatenation (Formal Systems)

This page is about Concatenation in the context of formal systems. For other uses, see Concatenation.

Definition

Concatenation is the process of placing elements of $\AA$ and words in $\AA$ next to each other to form a longer word.

Let $a, b, c \in \AA$.

Then concatenating $b$ to $a$ results in the word $ab$, and concatenating $c$ gives the word $abc$.

Concatenating $b$ then gives $abcb$.

Concatenating $aba$ to $aabcba$ gives the word $aabcbaaba$.

Let $A$ be the string $\text {dog}$.

Let $B$ be the string $\text {house}$.

Then concatenating $B$ to $A$ results in the string $\text {doghouse}$.

Results about concatenation in the context of formal systems can be found here.

The word concatenation derives from the Latin com- for with/together and the Latin word catena for chain.

However, the end result of such an operation is not to be confused with a (set theoretical) chain.